Consider a nite alphabet with a probability distribution p. We study the probability (p) of obtaining a palindrome in a nite time by independent draws. Using a Mahler equation for an associated generating function, we give a closed form expression for (p). Moreover we describe completely the cases where (p) has value less than 1, in connection with the singularities of the generating function. ...

Specialised literature presents a number of models describing the function of the vocal folds. In most of those models an emphasis is placed on the effect of Bernoulli’s air underpressure during the air passage through the glottis. The author defines a principle of the vocal folds function with a working version name „principle of the compressed air bubble“. The paper deals with the experimenta...

Based upon previous studies on laws of large numbers for fuzzy, random, fuzzy random and random fuzzy variables, We go further to explore weak law of large numbers(WLLN) for hybrid variables comprising fuzzy random variables and random fuzzy variables. we mainly prove Chebyshev WLLN, Poisson WLLN, Bernoulli WLLN, Markov WLLN and Khintchin WLLN for hybrid variables based on chance measure.

In this note we show how the properties of association and negative association can be combined with Stein’s method for compound Poisson approximation. Applications include k–runs in iid Bernoulli trials, an urn model with urns of limited capacity and extremes of random variables.

Abstract: For each n ≥ 1, let {Xn,j , j ≥ 1} be i.i.d. Bernoulli random variables with P{Xn,1 = 1} = pn = 1 − qn = 1 − P{Xn,1 = 0}, 0 < pn < 1. Define Wn,mn = ∑mn j=1 (Rn,j −an), where Rn,j = inf{k ≥ 0 : Xn,j+k = 0} is the number of success runs starting at j, mn is a sequences of positive integers, and an = pn/qn. We show that, under the condition mnpn → ∞, the central limit theorem Wn,mn σmn ...

— The so-called first fundamental transformation provides a natural combinatorial link between statistics involving cycle lengths of random permutations and statistics dealing with runs on Bernoulli sequences.

Let (b n) n≥0 be the binomial transform of (a n) n≥0. We show how a binomial transformation identity of Chen proves a symmetrical Bernoulli number identity attributed to Carlitz. We then modify Chen's identity to prove a new binomial transformation identity.